slighly upgraded version of arkham asylum
combat is way more better, you can actually block in 95% times.
more variaty in upgrades and they are actually useful and interesting comparing to AA
still a cinematic batman experience
cant say that "openworld" is better than linear AA its matter of taste.

now the problems:
stupid backtracking. for example you do side quest to find zsasz. to enter his room you need freeze BOMB. you will literally enter his hideout you will be super close to get him and he is literally threatining to kill the hostages. "I DONT HAVE EXACT GADGET I WILL COMEBACK HERE LATER" that BS just broke all the immersion and love to the game
sidequests are trash, half of them are random or requires pixel hunting. you will search random stuff without clues on the map just to get few min sequences with the villians. for example deadshot, you will expect cool ahh bossfight but instead you get minigame where you have to come closer to him and one shot him and it takes 15 seconds.
exploring is trash because of backtracking before you will get all the gadgets there is no point of exploring the map it kills all the joy of finding stuff and you leave it before you beat the game.
collecting riddles, doing challenges is UNREWARDING. if you get 400 riddles you will get segment with riddler but ITS BORING as already said its only takes few minutes of content. and when you collect everything and do the challenges YOU GET NOTHING (yes you get the additional info about characters and dialogues but ITS NOT COMPARABLE WITH TIME YOU WILL WASTE)
Your beloved steam lets you choose only between yes or no instead of score, stars, numbers so ofcourse I say yes but only for main campaign, skip all the BS and do me a favour, achievment hunting do not worth it, remember that.

spoilers?
also I forgot to say is that I liked from the beginning the character Hugo Strange. I thought it would be cool to fight him, there would be interesting and unique boss fight but instead game just wasted him without proper cool segment and saying that all this work is by Ras Al Ghoul that we already owned... wow........... okay.......... and we gonna boss fight Joker (clayface) that we already bossfighted in a first game.. because of the fan service....